| The finite difference method for the three-dimensional nonlinear coupled system of dynamics of fluids in porous media |
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| 引用本文： | YUAN Yirang Institute of Mathematics,Shandong University,Jinan 250100,China. The finite difference method for the three-dimensional nonlinear coupled system of dynamics of fluids in porous media[J]. 中国科学A辑(英文版), 2006, 49(2): 185-211. DOI: 10.1007/s11425-004-5209-6 |
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| 作者姓名： | YUAN Yirang Institute of Mathematics Shandong University Jinan 250100 China |
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| 作者单位： | YUAN Yirang Institute of Mathematics，Shandong University，Jinan 250100，China |
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| 摘 要： | For the three-dimensional coupled system of multilayer dynamics of fluids in porous media, the second-order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in l2 norm are derived to determine the error in the second-order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources.
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| 收稿时间： | 2004-09-28 |
| 修稿时间： | 2005-07-12 |
The finite difference method for the three-dimensional nonlinear coupled system of dynamics of fluids in porous media |
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| YUAN Yirang. The finite difference method for the three-dimensional nonlinear coupled system of dynamics of fluids in porous media[J]. Science in China(Mathematics), 2006, 49(2): 185-211. DOI: 10.1007/s11425-004-5209-6 |
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| Authors: | YUAN Yirang |
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| Affiliation: | Institute of Mathematics, Shandong University, Jinan 250100, China |
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| Abstract: | For the three-dimensional coupled system of multilayer dynamics of fluids in porous media, the second-order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in l2 norm are derived to determine the error in the second-order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources. |
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| Keywords: | multilayer coupled system nonlinear equations upwind finite difference fractional steps convergence numerical simulation |
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